Consider the function below. lim x ->1 3x+2=5 What values of x guarantee that f(x)=3x+2 is within 0.04 unit of 5?
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f(1+h)=3(1+h)+2=3+3h+2=5+0.04 where h is the discrepancy in x and 0.04 the discrepancy in the result 5.

So 5+3h=5+0.04, h=0.04/3=0.013, and x must be within 0.013 units of 1. That is, x=1±0.013 or 0.987<x<1.013.

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